The great migration began perhaps 40 years ago. From strongholds in the Rocky Mountains and Texas, young males headed east, seeking female companionship and new places to settle.

The emigrants were about seven feet long, nose to tail, and weighed up to 160 pounds. Given a dietary choice, they preferred deer, but would eat almost anything that moved: elk, bighorn sheep, wild horses, beaver, even porcupines. Left free for an evening, they were capable of killing a dozen domestic sheep before dawn, eating their fill and leaving the rest for the buzzards. They were also known to attack humans on occasion.

Long ago the Inca called them puma, but today — though they belong to only one species — they have many names. In Arizona they are known as mountain lions; in Florida they are panthers, and elsewhere in the South they are called painters. When they roamed New England, they were called catamounts. In much of the Midwest they are known as cougars, and that is the name everyone understands.

Until relatively recently, they were mainly a memory. All but exterminated east of the Rockies by 1900, they were treated as “varmints” in most Western states until the late ’60s and could be shot on sight. In Maine, the last catamount was killed in 1938.

But today Puma concolor is back on the prowl. That is one of the great success stories in wildlife conservation, but also a source of concern among biologists and other advocates, for their increasing numbers make them harder to manage — and harder for people to tolerate. No reliable estimate exists for the cougar population at its lowest point, before the 1970s, but there are now believed to be more than 30,000 in North America. They have recolonized the Black Hills of South Dakota, the North Dakota Badlands and the Pine Ridge country of northwestern Nebraska.

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A young male cougar was tranquilized after it was found stuck in a concrete-walled aqueduct near downtown Santa Cruz, Calif., in May.Credit
Dan Coyro/Santa Cruz Sentinel, via Associated Press

There are increasing reports of sightings in 11 Midwestern states, as well as in Arkansas and Louisiana. A young male tripped a trail camera in the Missouri Ozarks on Feb. 2, and dogs treed one in Minnesota in March.

“Every year we see more of them,” said Mark Dowling, a founder of the Cougar Network, a nonprofit research group and a leading source of online information about cougars. “It used to be a rarity when a mountain lion showed up in Missouri. It’s almost routine now.”

And as cougars migrate eastward, they are likely to wear out their welcome. People in states unaccustomed to these outsize prowlers will have to answer unpleasant questions: How many livestock and game animals are people willing to lose? How dangerous are cougars to pets and children? How much disruption is a small community willing to endure?

“A lot of state conservation agencies are looking into how to prepare for recolonization,” said Clay Nielsen, a wildlife biologist at Southern Illinois University and the director of scientific research for the Cougar Network. Surveys he conducted in Illinois, North Dakota and Kentucky found “the public more supportive than I would have guessed.” But as the big cats become more plentiful, he added, “attitudes are probably going to change.”

The center of cougar genetic diversity is in Brazil, but the Western Hemisphere has six robust subspecies in all.The Florida panther was listed as endangered in 1995, when eight Texas female cougars were released in South Florida in a last effort to save them from extinction. It worked. The Florida panther, it turned out, is a North American cougar whose kinked tails, heart defects, small litters and short lives were consequences of prolonged inbreeding. From fewer than 30 in 1995, the panther population in southwestern Florida has grown to more than 150.

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Melanie Culver, a wildlife geneticist at the University of Arizona, says the cougar appears to have evolved about 300,000 years ago from a cheetahlike cat that is now extinct. When Europeans arrived in the Americas, cougars were everywhere, but human predation and the loss of habitat to agriculture took a heavy toll.

Dr. Nielsen said, “By 1900, we had basically killed them all off in the East and Midwest.”

Cougars are solitary predators whose hunting ground can vary widely in size, depending on available prey, water supply and cover. They like woodland and high country, but can handle almost any habitat that offers concealment, including desert (Arizona), swamp (Florida), prairie (Nebraska), temperate rain forest (Washington State) and the Pacific Coast. National Park Service biologists tagged a pair of cougar kittens last year near Malibu, Calif.

Cougar offspring stay with their mothers up to two years. After that the young males tend to disperse, partly to avoid other males in their home territory and partly to lower the odds of inbreeding. After cougars filled up the mountain states and West Texas, the young males began to travel east. (Females also move, but tend to stay closer to home.)

Cougars are not cuddly. Jw Nuckolls, a rancher in northeastern Wyoming, lost 15 sheep one night to a single cougar, and 32 to cougar predation in two months in 2011.

During an aerial survey at the Kofa National Wildlife Refuge in southwestern Arizona in 2000, “what looked like three golden retrievers” were spotted on a stone outcrop, recalled Susanna Henry, the refuge manager. They were cougars — probably mother and children.

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A print of an American cougar, made around 1850.Credit
Hulton Archive/Getty Images

“In the following years the population of bighorn sheep at the refuge began to decline precipitously, from 800 at the turn of the century to 620 in 2003 and 390 in 2006,” Ms. Henry said. Since then, the sheep count appears to have stabilized at a bit over 400.

Despite their propensity to wreak havoc on other wildlife and livestock (they will take on animals up to seven times their own size, including full-grown elk, horses and steers), cougars are regarded as a manageable nuisance by ranchers and offered a respect that wolves, the West’s other legendary marauders, can only dream about.

There is no easy explanation for this. Dr. Nielsen noted that Europeans had no experience with big cats when they arrived in the New World, but had long vilified the “big bad wolf.” Wolves, he said, “had a bad rap.”

“Cougar are easier to hunt” than wolves “and easier to control,” he said. Cougars run from wolves and will run from barking dogs. Hunters use hounds to tree them. They are predictable, while wolves are not.

But if cougars are easier to control now, “things will change,” said Harley G. Shaw, a retired wildlife biologist for the Arizona Game and Fish Department and an author of a cougar field guide now in its fourth printing. “That time may even be here now.”

Arizona and New Mexico deliberately cull cougars to protect their bighorn sheep, he said, and added: “Most desert bighorn ranges are small and isolated under the best conditions. One or two lions can have a big impact.”

A version of this article appears in print on June 11, 2013, on page D1 of the New York edition with the headline: A Glamorous Killer Returns. Order Reprints|Today's Paper|Subscribe